Question

(2^10×3^7)^9 : (2^5×3^6)^10 =

Answer 1

   
[tex]\displaystyle \\ \\ (2^{10}\times 3^7)^9 : (2^5\times 3^6)^{10} = \\ \\ =\frac{(2^{10}\times 3^7)^9}{(2^5\times 3^6)^{10}} = \\ \\ =\frac{(2^{10})^9 \times (3^7)^9}{(2^5)^{10} \times (3^6)^{10}} = \\ \\ =\frac{2^{10 \times 9} \times 3^{7 \times 9}}{2^{5 \times 10}\times 3^{6 \times 10}} = \\ \\ =\frac{2^{90} \times 3^{63}}{2^{50 }\times 3^{60}} = 2^{90-50} \times 3^{63-60}= \boxed{2^{40} \times 3^3}[/tex]